{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Bridges and Trolls"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "bridges = ['TTGGG', 'TGGGG', 'GGGGG']\n",
      "bridge_pvals = [0.2, 0.2, 0.6]\n",
      "\n",
      "def capture_creature(creatures):\n",
      "    \"\"\"Captures and returns a random creature and removes it from the list.\"\"\"\n",
      "    index = np.random.randint(len(creatures))\n",
      "    return creatures.pop(index)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "results = []\n",
      "\n",
      "num_safe = 0\n",
      "num_trolls_picked = 0\n",
      "while num_trolls_picked < 100000:\n",
      "    bridge = np.random.choice(bridges, 1, bridge_pvals)[0]\n",
      "    creatures = list(bridge)\n",
      "    captured_creature = capture_creature(creatures)\n",
      "    if captured_creature == 'T':\n",
      "        num_trolls_picked += 1\n",
      "        if 'T' not in creatures:\n",
      "            num_safe += 1\n",
      "        results.append(num_safe / float(num_trolls_picked))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(results)\n",
      "plt.ylim(.3, .36)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "(0.3, 0.36)"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AAQjmAAAAgAMQzAEAAAAHIJgDAAAADkAwBwAAAByAYA4AAAA4AMEcAAAAcACCOQAAAOAA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\nCm1ebbOwAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9862e4c>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print results[-1]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.33168\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Gift Boxes"
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Part A: Picked a box and picked an item. It was valuable! What did we learn about the number of valuable boxes? The distribution skews towards there being more valuable boxes."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# priors[i] is the probability of there being i boxes with 90% valuable items\n",
      "priors = np.array([.0, .05, .20, .25, .20, .20, .10, 0, 0, 0, 0, 0, 0, 0])\n",
      "print priors.sum()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1.0\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# P(Data | H_i)\n",
      "p_data_given_hyp = []\n",
      "for hyp in xrange(14):\n",
      "    p_data_given_hyp.append((9 / 10.0) * (hyp / 13.0) + (2 / 10.0) * (13 - hyp) / 13.0)\n",
      "print p_data_given_hyp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[0.2, 0.2538461538461539, 0.3076923076923077, 0.3615384615384616, 0.4153846153846154, 0.4692307692307693, 0.5230769230769231, 0.576923076923077, 0.6307692307692307, 0.6846153846153846, 0.7384615384615386, 0.7923076923076923, 0.8461538461538463, 0.9]\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# P(Data)\n",
      "p_data = np.dot(priors, p_data_given_hyp)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "posteriors = (p_data_given_hyp * priors) / p_data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(priors, label='prior')\n",
      "plt.plot(posteriors, label='posterior')\n",
      "plt.xlim(0, 13)\n",
      "plt.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<matplotlib.legend.Legend at 0x9b4cc8c>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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EZIa4uQkZRE4OsGYNcOaMtPNszdyKJ72ehPsT7tJOJKKlS4GwsDbIyNiEw7cT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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x9b3a74c>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "Now we pick another random item from the same box. What is the probability it's valuable?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p_valuable = 0.0\n",
      "for hyp in xrange(14):\n",
      "    p_valuable += posteriors[hyp] * ((8 / 9.0) * (hyp / 13.0) + (1 / 9.0) * (13 - hyp) / 13.0)\n",
      "    \n",
      "print p_valuable"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.342364449786\n"
       ]
      }
     ],
     "prompt_number": 11
    }
   ],
   "metadata": {}
  }
 ]
}